How to find the square root of 128
2 answers:
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9514 1404 393
Answer:
- ∠PAO = 90°
- ∠APO = 30°
- ∠AOB = 120°
- PB ≈ 8.7
Step-by-step explanation:
A tangent makes a right angle with the radius to the point of tangency. Hence ∠PAO is 90°. The ratio of the short side (OA) of the right triangle OAP to the hypotenuse (OP) is 5 : 10 = 1 : 2. These are the ratios found in a 30°-60°-90° triangle, so we know that ∠APO = 30°.
OP is a bisector of angle APB, so that angle is 60°. Angle AOB is the supplement to angle APB, so ∠AOB = 120°.
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As we said above, triangle OAP is a 30°-60°-90° triangle, so its side lengths have the ratios 1 : √3 : 2. This means PA = PB = 5√3 ≈ 8.7.
Answer:
- C. 144 + 36√3
Step-by-step explanation:
<u>Area formula for equilateral triangle with side a:</u>
- A = √3/4a²
<u>The base area is:</u>
- A = √3/4*12² = 36√3
The three lateral surfaces have same sides of 10, 10 and 12.
<u>Find each surface area using heron's formula:</u>
- s = P/2 = (10 + 10 + 12)/2 = 16
- s - a = 16 - 10 = 6
- s - b = 6
- s - c = 16 - 12 = 4
<u>Total surface area is:</u>
- 48*3 + 36√3 =
- 144 + 36√3
Correct choice is C